Mass matters for standing waves on a string?

In summary, the mass of a string plays a significant role in the formation and characteristics of standing waves. It affects the frequency, wavelength, tension, and energy of the waves, which can impact the number of standing waves, their amplitude, and the harmonics present on the string. Changing the mass of the string can alter these factors, resulting in different patterns of standing waves.
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zooch
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Homework Statement
Does the equation of motion of a standing wave get impacted when a mass is attached to the string?
Relevant Equations
y = A cos(Wt)
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The question is to explain the equation of motion of the red ball. The string is massless and a small ball of mass m is attached to the string halfway. I just assumed the mass of the string is the same as the mass of the ball and explained the equation A cos(Wt) by defining the terms. I'm not sure if the small ball changes anything...
 
Last edited:
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FAQ: Mass matters for standing waves on a string?

What is a standing wave on a string?

A standing wave on a string is a type of wave that is formed when two waves with the same frequency and amplitude travel in opposite directions on a string. This causes the string to vibrate at specific points, called nodes, while remaining still at other points, called antinodes.

How does mass affect standing waves on a string?

The mass of the string affects the speed at which waves travel on it. A heavier string will have a lower wave speed, which will result in longer wavelengths and lower frequencies for standing waves. This means that the standing wave pattern will appear stretched out on a heavier string compared to a lighter string.

How does the tension of the string affect standing waves?

The tension of the string also affects the speed of waves traveling on it. A higher tension will result in a higher wave speed, which will lead to shorter wavelengths and higher frequencies for standing waves. This means that the standing wave pattern will appear more compressed on a string with higher tension compared to one with lower tension.

What is the relationship between mass, tension, and frequency in standing waves?

The frequency of a standing wave on a string is directly proportional to the tension of the string and inversely proportional to the mass per unit length of the string. This means that as the tension increases, the frequency of the standing wave also increases, while an increase in mass per unit length will result in a decrease in frequency.

Can the length of the string affect standing waves?

Yes, the length of the string also plays a role in determining the frequency of standing waves. The longer the string, the longer the wavelength and the lower the frequency of the standing wave. This is because longer strings have more nodes and antinodes, resulting in a lower frequency of vibration.

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